# Statistics for Environmental Engineers

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A common question is: “Are the differences between labs large enough to have important consequences in practice?” Importance and statistical significance are different concepts. Importance depends on the actual use to which the measurements are put. Statistically significant differences are not always important. We can change significance to nonsignificance by changing the probability level of the test (or by using a different statistical procedure altogether). This obviously would not change the practical importance of a real difference in performance. Furthermore, the importance of a difference will exist whether we have data to detect it or not.

Analysis of variance can be applied to problems having many factors. One such example, a four-way ANOVA, is discussed in Chapter 26. Chapter 25 discusses the use of ANOVA to discover the relative magnitude of several sources of variability in a sampling and measurement procedure. Box et al. (1978) provide an interesting geometric interpretation of the analysis of variance.

### References

Box, G. E. P., W. G. Hunter, and J. S. Hunter (1978). Statistics for Experimenters: An Introduction to Design, Data Analysis, and Model Building, New York, Wiley Interscience.

Johnson, R. A. and D. W. Wichern (1992). Applied Multivariate Statistical Analysis, Englewood Cliffs, NJ, Prentice-Hall.

Sokal, R. R. and F. J. Rohlf (1969). Biometry: The Principles and Practice of Statistics in Biological Research, New York, W. H. Freeman and Co.

### Exercises

24.1 Chromium Measurements. A large portion of chromium contaminated water was divided into 32 identical aliquots. Eight aliquots were sent to each of four laboratories and the following data were produced. Are the laboratories making consistent measurements?

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